Prediction of Network Controllability Robustness Based on Graph Neural Network
Kunpeng Wang, Shaopeng Pang, Xinghui Wang, Cheng Liu, Yongguo Zhao, Hengqing Yang, Gengwei Zhao · 2024
The controllability of complex networks has received extensive attention and in-depth research. The problem of controllability robustness is an important topic in the research on the controllability of networks. We propose a graph neural network model for network controllability robustness (NCR-GNN), which aims to predict the proportion of critical edges in networks, which is a key indicator for quantifying the controllability robustness of networks. The NCR-GNN model is a multi-layer graph neural network architecture that incorporates an average degree encoder. This encoder provides an initial feature embedding for the graph, utilizing both node degree and global degree information to efficiently capture the network's structural characteristics at both local and global levels. We incorporate aggregation methods derived from several well-established graph neural network (GNN) models, including the Graph Convolutional Network (GCN), Graph Attention Network (GAT), Graph Isomorphism Network (GIN), Chebyshev Network (ChebNet) and Topology Adaptive Graph Convolutional Network (TAG) into the NCR-GNN framework. Experimental results based on models and real networks show that the NCR-GNN model based on the ChebNet-aggregation method outperforms others in terms of training, validation, and test performance, demonstrating excellent generalization capabilities. This shows that the NCR-GNN model based on the ChebNet-aggregation method is suitable for the prediction task of network controllability robustness. Our NCR-GNN model provides an effective and adaptable framework to predict network controllability robustness, which has important potential applications in network science and engineering.